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Availability in Stochastic Models

  1. Sophie Mercier

Published Online: 14 JAN 2011

DOI: 10.1002/9780470400531.eorms0073

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Mercier, S. 2011. Availability in Stochastic Models. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques et de leurs Applications–PAU (UMR CNRS 5142), Bâtiment IPRA, Pau cedex, France

Publication History

  1. Published Online: 14 JAN 2011

Abstract

A system is considered, which evolves in time according to a stochastic process. The system state space is divided into up- and down-states and the quantities of interest are the system point and asymptotic availabilities, namely the probabilities that the system is in an up-state at some finite time t and as t goes to infinity. Different stochastic continuous-time models and associated tools are presented, such as alternating renewal models, Markov and semi-Markov models, regenerative and Markov regenerative models, with the corresponding renewal or Markov renewal equations fulfilled by the point availability. Classical limit theorems then allow to derive expressions for the asymptotic availability, which involve the process on a generic (Markov) cycle.

Keywords:

  • reliability;
  • availability;
  • renewal theory;
  • Markov renewal theory